My homework assignment has asked me to prove that $\lfloor-x\rfloor = -\lceil x\rceil$.
Conceptually this makes perfect sense to me, I just am at a loss for how to start actually proving it. I figure that it has something to do with these definitions: $$\lfloor x \rfloor: a \le x \lt a+1$$ $$ \lceil x \rceil : a \lt x \le a+1 $$
But I'm unsure of how to apply these to devise a proof for this. Any help that anyone could give would be incredibly appreciated, I've spent way too much time staring at the question trying to figure it out.